TY - GEN
T1 - Bounds on the Capacity of PIR over Graphs
AU - Sadeh, Bar
AU - Gu, Yujie
AU - Tamo, Itzhak
N1 - Publisher Copyright:
© 2021 IEEE.
PY - 2021/7/12
Y1 - 2021/7/12
N2 - In the private information retrieval (PIR) problem, a user wants to retrieve a file from a database without revealing any information about the desired file's identity to the servers that store the database. In this paper, we study the PIR capacity of a graph-based replication system, in which each file is stored on two distinct servers according to an underlying graph. This paper aims to provide upper and lower bounds to the PIR capacity of graphs via various graph properties. In particular, we provide several upper bounds on the PIR capacity that apply to all graphs. We further improve the bounds for specific graph families (which turn out to be tight in certain cases) by utilizing the underlying graph structure. For the lower bounds, we establish optimal rate PIR retrieval schemes for star graphs via edge-coloring techniques. Lastly, we provide an improved PIR scheme for complete graphs, which implies an improved general lower bound on all graphs' PIR capacity.
AB - In the private information retrieval (PIR) problem, a user wants to retrieve a file from a database without revealing any information about the desired file's identity to the servers that store the database. In this paper, we study the PIR capacity of a graph-based replication system, in which each file is stored on two distinct servers according to an underlying graph. This paper aims to provide upper and lower bounds to the PIR capacity of graphs via various graph properties. In particular, we provide several upper bounds on the PIR capacity that apply to all graphs. We further improve the bounds for specific graph families (which turn out to be tight in certain cases) by utilizing the underlying graph structure. For the lower bounds, we establish optimal rate PIR retrieval schemes for star graphs via edge-coloring techniques. Lastly, we provide an improved PIR scheme for complete graphs, which implies an improved general lower bound on all graphs' PIR capacity.
UR - http://www.scopus.com/inward/record.url?scp=85115106345&partnerID=8YFLogxK
U2 - 10.1109/ISIT45174.2021.9518086
DO - 10.1109/ISIT45174.2021.9518086
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AN - SCOPUS:85115106345
T3 - IEEE International Symposium on Information Theory - Proceedings
SP - 1913
EP - 1918
BT - 2021 IEEE International Symposium on Information Theory, ISIT 2021 - Proceedings
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 2021 IEEE International Symposium on Information Theory, ISIT 2021
Y2 - 12 July 2021 through 20 July 2021
ER -